q-integral and moment representations for q-orthogonal polynomials

Mourad E.H. Ismail, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

Original languageEnglish (US)
Pages (from-to)709-735
Number of pages27
JournalCanadian Journal of Mathematics
Volume54
Issue number4
DOIs
StatePublished - Aug 2002

Keywords

  • Al-Salam-Chihara polynomials
  • Associated polynomials
  • Continuous q-ultraspherical polynomials
  • Generating functions
  • q-difference equations
  • q-integral
  • q-orthogonal polynomials

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